Modern day signal, image, and information processing increasingly relies on the use of matrix algebra as one of its basic computational tools. In addition, many of today's problems require a real-time computational capability as well. As a consequence, current emphasis is placed on the development of dedicated electronic parallel processing devices using VLSI/VHSIC technology to perform the intensive computations required in numerical matrix algebra. Based on the proliferation of journal articles in this field over the past five years, a growing interest in the use of optical processing techniques to perform matrix operations is materializing. Optics, with its innate parallelism, noninterfering communication and high bandwidth, has successfully demonstrated its strengths in the past two decades to perform convolutions and correlations, as well as a variety of linear transform operations. However, to assure that optical processing has a significant impact on general matrix computation, new concepts and devices are being formulated and conceived which improve the precision of computations performed optically.
One technique which has demonstrated improved optically performed precision of computations employs an algorithm to perform fixed-point multiplications and additions and uses optical convolving devices as set out by H. J. Whitehouse and J. M. Speiser in their article entitled "Linear Signal Processing Architectures" Aspects of Signal Processing with Emphasis on Underwater Acoustics, G. Tacconi, Ed. (Reidel, Dordrecht, 1977), Part II and by D. Psaltis, D. Casasent, D. Neft and M. Carlotto in their article entitled "Accurate Numerical Computation by Optical Convolution," SPIE, Vol. 232, pp. 151-156, 1980. The algorithm of these two articles has gained popularity as the digital multiplication by analog convolution (DMAC) algorithm. For the case of radix 2, for example, the DMAC algorithm is novel in that binary numbers may be added without carries if the output is allowed to be represented in a mixed binary format. In the mixed binary format, like binary arithmetic, each digit is weighted by a power of 2, but unlike binary arithmetic, the value of each digit can be greater than 2. Eliminating the need for carries makes this technique particularly attractive in terms of optical implementation. The DMAC algorithm has been used in optical architectures to perform matrix multiplication involving numbers expressed in fixed-point form. Examples of such use are set out in numerous articles such as the presentation of W. C. Collins, R. A. Athale, and P. D. Stilwell in "Improved Accuracy for an Optical Iterative Processor", SPIE Vol. 352, pp. 59-66, 1982 in the article by R. P. Bocker, S. R. Clayton and K. Bromley in "Electro Optical Matrix Multiplication Using the Twos Complement Arithmetic for Improved Accuracy" Applied Optics, Vol. 22, pp. 2019-2021, 1983, in the article by P. S. Guilfoyle in "Systolic Acousto-Optic Binary Convolver" Optical Engineering Vol. 23, pp. 20-25, 1984 and by A. P. Goutzoulis in "Systolic Time-Integrating Acoustooptic Binary Processor" Applied Optics, Vol. 23, pp. 4095-4099, 1984. The most often heard criticism of the DMAC algorithm, when used in matrix multiplication, is the complication arising from the need for high-speed electronic analog-to-digital converters for converting the mixed binary back to binary form.
In a recent advancement H. J. Caulfield has provided an "existence proof" for optical floating-point matrix algebra in his article entitled "Floating Point Optical Matrix Calculations" Optical Engineering Vol. 22, No. 6, pp. 765-766, November-December 1983 (he expounds on the feasibility of floating point optical matrix-vector multiplication calculations).
Thus there exists in the state-of-the-art a continuing need for an implementation of the DMAC algorithm to perform matrix-vector multiplications involving matrices and vectors whose elements are represented in binary floating-point form and an acousto-optical time-integrated architecture to implement the DMAC algorithm as well as a technique to eliminate the need for analog-to-digital converters at the optical processor back-end.